A method and system for constructing a business data warehouse for a city digital base map

By analyzing the GIS vector data of the city's digital base map, calculating the dimensional bit sequence offset and correlation feature coefficient, and building a spatiotemporal data warehouse, it solves the problem of inefficient retrieval efficiency caused by inconsistent quality of digital base maps in smart cities, and improves the correlation of data and query efficiency.

CN118981508BActive Publication Date: 2024-12-17HUNAN TIANXIANGHE INFORMATION TECH CO LTD
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Patent Information

Application Number
CN202411471821.3
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-10-22
Publication Date
2024-12-17
Estimated Expiration
2044-10-22

AI Technical Summary

Technical Problem

In the process of digitalization of smart cities, due to inconsistent collection equipment and software versions, the quality of the city's digital base map is uneven, resulting in inefficient search and query of business data warehouses.

Method used

By collecting GIS vector data of the city digital base map, obtaining the three-dimensional digital base map matrix, calculating the dimension bit sequence offset and correlation feature coefficient, building a city business data collection, and using ETL tools to build a city spatio-temporal data warehouse to optimize data storage and Query.

Benefits of technology

It improves the overall correlation of urban business data under spatial distribution, ensures the correlation attributes in the data storage process, and optimizes query retrieval efficiency.

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Abstract

The present application relates to the field of data processing technology, and specifically to a method and system for constructing a business data warehouse of a city digital base map, the method comprising: collecting GIS vector data of the city digital base map at each time; constructing a three-dimensional digital base map matrix of a preset size; and then obtaining the dimension vectors of each window in the digital base map dimension plane matrix of each vector dimension; calculating the dimensional order offset between each vector dimension; obtaining the correlation characteristic coefficient between each vector dimension and other vector dimensions; obtaining the city information correlation characteristic coefficient of each vector dimension based on the correlation characteristic coefficient; obtaining the city business data set of each vector dimension based on the city information correlation characteristic coefficient, and constructing a city spatiotemporal data warehouse. The present application improves the overall efficiency of city business data query and retrieval.
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Description

Technical Field

[0001] The present application relates to the field of data processing technology, and in particular to a method and system for constructing a business data warehouse for a city digital base map. Background Art

[0002] With the rapid development of computer hardware, the data processing capabilities of computer-related intelligent terminal devices have been continuously improved, and the response speed of data tasks has been continuously accelerated. Therefore, with the rapid development of new-generation information technology, mainly the Internet of Things, cloud computing and artificial intelligence, the digital process of urban operation and management has also entered a stage of rapid advancement. Digital smart cities have effectively solved the problems of information blockage and data sharing difficulties in the process of urban management, and broken down the digital information barriers between departments in the process of urban management.

[0003] However, in the process of smart city digitization, due to inconsistent collection equipment and software versions, the quality of urban digital base maps is uneven, and there is invalid redundant information in the urban digital base map information. In this case, the business data warehouse constructed will have low efficiency in retrieval and query between business data. Summary of the invention

[0004] In order to solve the above technical problems, the purpose of this application is to provide a method and system for constructing a business data warehouse for a city digital base map. The technical solutions adopted are as follows:

[0005] In a first aspect, an embodiment of the present application provides a method for constructing a business data warehouse of a city digital base map, the method comprising the following steps:

[0006] Collect various GIS vector data of the city digital base map at each time as each vector dimension; obtain the three-dimensional digital base map matrix of the city digital map at each time; the matrix is ​​composed of two-dimensional geographical location coordinates and each vector dimension at the corresponding coordinate position;

[0007] Based on the three-dimensional digital base map matrix, dimension vectors of different windows in the digital base map dimension plane matrix of each vector dimension are obtained; based on the difference between the maximum values ​​of the dimension vectors of the same window in the vector dimension, the dimension sequence offset between any two different vector dimensions of the same window is obtained;

[0008] Based on the dimension order offset and the similarity between the dimension vectors, the correlation feature coefficients between each vector dimension and all other vector dimensions of the same window are obtained;

[0009] Based on the correlation characteristic coefficient, obtain the city information correlation characteristic coefficient of each vector dimension; based on the city information correlation characteristic coefficient, obtain the city business data set of each vector dimension;

[0010] Build an urban spatiotemporal data warehouse based on urban business data sets.

[0011] Furthermore, the GIS vector data includes: terrain height, building density, traffic volume, population density, number of shopping malls and number of schools.

[0012] Furthermore, the digital base map dimension plane matrix includes:

[0013] The two-dimensional matrix under each vector dimension in the three-dimensional digital base map matrix serves as the digital base map dimension plane matrix of each vector dimension.

[0014] Furthermore, the method for obtaining the dimension vector is:

[0015] For the digital base map dimension plane matrix of each vector dimension in the three-dimensional digital base map matrix, a window with different preset side lengths is constructed with the central pixel point of the digital base map dimension plane matrix as the center;

[0016] For windows with different preset side lengths, the data of the window edge pixels in the digital base map dimension plane matrix are selected to construct the dimension vectors of the corresponding vector dimensions in windows with different preset side lengths.

[0017] Furthermore, the method for obtaining the dimension sequence offset is:

[0018] For windows with the same preset side length, obtain the order of the maximum value in the dimensional vector of each vector dimension as the first maximum order of the dimensional vector of each vector dimension, and calculate the absolute value of the difference between the first maximum orders of any two different vector dimensions as the dimensional order offset between any two different vector dimensions.

[0019] Further, the method for obtaining the correlation characteristic coefficient is:

[0020] In any window with the same preset side length, for any vector dimension, calculate the similarity between the dimensional vectors of any vector dimension and other vector dimensions, take the product of the dimensional sequence offset between any vector dimension and other vector dimensions and the similarity as the first product, and take the sum of all the first products of any vector dimension as the associated characteristic coefficient of any vector dimension in the same window.

[0021] Furthermore, the method for obtaining the city information correlation characteristic coefficient is:

[0022] For each vector dimension, the sum of the correlation characteristic coefficients of all windows in the vector dimension is used as the city information correlation characteristic coefficient of each vector dimension.

[0023] Furthermore, the method for acquiring the city business data set is:

[0024] For each vector dimension in the three-dimensional digital base map matrix, the distance between any two pixel points in the vector dimension is calculated as the first distance;

[0025] The product of the first distance between any two pixel points in the vector dimension and the city information association characteristic coefficient in the vector dimension is taken as the equivalent distance between any two pixel points;

[0026] Using a clustering algorithm, clustering is performed by taking the equivalent distance as the metric distance between any two pixel points to obtain a preset number of clusters;

[0027] For each cluster, the sum of equivalent clusters between any two pixels in the cluster is calculated as the first equivalent sum, and the set of pixels in the cluster with the smallest first equivalent sum is taken as the urban geographic spatial information data set.

[0028] Further, the construction of the urban spatiotemporal data warehouse according to the urban business data set includes:

[0029] For the urban business data set obtained from the digital base map GIS vector data at each moment, the data in the urban business data set is used as the data in the source library, and the ETL tool is used to process the data in the source library to obtain standard base map data and save it in the governance library;

[0030] The data in the governance library is processed, and the data that meets the preset standard results requirements are synchronized to the standard library in chronological order according to the time of the urban business data set. Other updated and abolished data are saved in the historical library to complete the construction of the urban spatiotemporal data warehouse.

[0031] In the second aspect, an embodiment of the present application also provides a business data warehouse construction system for a city digital base map, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor implements the steps of any one of the above-mentioned methods when executing the computer program.

[0032] This application has at least the following beneficial effects:

[0033] The technical solution of the present application analyzes the changing state of urban business data in the geographic space dimension, calculates the urban geographic space dimension rank offset, calculates the change in the numerical deviation of urban business data in the geographic space dimension, and improves the overall distribution state of data in space. Furthermore, the technical solution of the present application combines the urban geographic space dimension rank offset in the three-dimensional digital base map matrix, and uses the urban geographic space dimension rank offset combined with the dimension association attribute in the three-dimensional digital base map matrix to analyze and calculate the data attributes of urban business data in different vector dimensions, thereby improving the overall association of urban business data in spatial distribution, ensuring the association attributes in the storage process of related data, and optimizing and improving the overall efficiency of urban business data query and retrieval. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present application or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0035] Figure 1 A flowchart of a method for constructing a business data warehouse for a city digital base map provided in one embodiment of the present application;

[0036] Figure 2 A schematic diagram of dimensional vector data arrangement provided for one embodiment of the present application;

[0037] Figure 3 A flowchart for obtaining a city business data set provided by an embodiment of the present application;

[0038] Figure 4 A schematic diagram of constructing a city spatiotemporal data warehouse provided in one embodiment of the present application. DETAILED DESCRIPTION

[0039] In order to further explain the technical means and effects adopted by the present application to achieve the predetermined invention purpose, the following is a detailed description of the business data warehouse construction method and system of a city digital base map proposed in the present application, its specific implementation method, structure, features and effects, in combination with the accompanying drawings and preferred embodiments. In the following description, different "one embodiment" or "another embodiment" does not necessarily refer to the same embodiment. In addition, specific features, structures or characteristics in one or more embodiments may be combined in any suitable form.

[0040] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0041] The following is a detailed description of a specific solution of a business data warehouse construction method and system for a city digital base map provided by the present application in conjunction with the accompanying drawings.

[0042] See also Figure 1 , which shows a flowchart of a method for constructing a business data warehouse of a city digital base map provided by an embodiment of the present application, the method comprising the following steps:

[0043] Step S1, obtaining the city digital base map GIS vector data.

[0044] Through various satellites, sensors, and mobile terminal devices, we can obtain massive spatiotemporal data related to urban construction, transportation, and commercial industries in the process of urban digital management.

[0045] Massive spatiotemporal data include data of various structural types, among which digital base map GIS data are mostly vector data. The digital base map of this application is represented by raster data, and the digital base map GIS vector data of each moment is collected. In order to more comprehensively reflect the dynamic changes in urban business, the data types of each pixel point in the digital base map GIS vector data are: terrain height, building density, traffic flow, population density, number of shopping malls and number of schools.

[0046] At this point, the city digital base map GIS vector data is obtained.

[0047] Step S2, based on the city digital base map GIS vector data, obtain the dimensional vector of each window in the digital base map dimensional plane matrix of each vector dimension; then obtain the dimensional order offset between each vector dimension; calculate the correlation characteristic coefficient between each vector dimension and other vector dimensions based on the dimensional order offset and the similarity between the dimensional vectors; then obtain the city information correlation characteristic coefficient of each vector dimension based on the correlation characteristic coefficient, and then construct the city business data set of each vector dimension.

[0048] The spatial location information of the city changes accordingly with the population density distribution, and the functional buildings in different geographic spatial areas in the city space will also change dynamically with the population distribution. Geographical attributes such as urban building clusters, functional planning areas, economic business areas and transportation routes will continue to change over time. Therefore, the urban digital base map GIS data obtained through the urban business data aggregation library has obvious spatiotemporal change properties.

[0049] Since the changes in the coordinate positions of urban building clusters and different areas should have a more obvious spatial continuity, such as the development and utilization of land, the extension and expansion of urban roads and other dynamic changes and continuity, in order to improve the effective storage of massive urban business data during the storage process, it is necessary to further calculate the geographic space changes in the urban business data.

[0050] The numerical values ​​of different pixel positions in the digital base map grid reflect the changing characteristics of the current building cluster area. The numerical characteristics of the digital base map grid data of building clusters with close spatial locations should also be relatively close. Since the dimensional coverage of urban business data is relatively comprehensive, for digital base map grid data with high-dimensional information, in order to optimize the data structure storage performance in the business database and improve the ability to quickly retrieve effective information in the business database, the effective data information feature dimensions in the digital base map business database are first calculated.

[0051] For the urban digital base map within the local range area, the correlation characteristics between different vector dimension information in the digital base map raster within the local range area are analyzed.

[0052] Specifically, in the city digital base map at each time, each GIS vector data is used as each vector dimension to construct a b The three-dimensional matrix of c is recorded as the three-dimensional digital base map matrix. In the three-dimensional digital base map matrix, the two-dimensional matrix of each vector dimension represents the data information under the current vector dimension. In this embodiment, the value of a is 9, the value of b is 9, and the value of c is 6. The implementer can select other values ​​according to the actual situation.

[0053] The two-dimensional matrix of each vector dimension of each GIS vector data is recorded as the digital base map dimension plane matrix of each vector dimension. Each element in the digital base map dimension plane matrix represents the data information of the corresponding vector dimension at different spatial positions in the local area.

[0054] Since the distribution of local geographic spatial information in a city is highly correlated, the information change patterns at different locations will also have certain different attributes.

[0055] Furthermore, for the digital base map dimension plane matrix of each vector dimension in the three-dimensional digital base map matrix, a window with a side length of m is constructed with the central pixel point of the digital base map dimension plane matrix as the center, where the values ​​of m are 3, 5, 7, and 9 respectively; for windows with different side lengths, the data of the window edge pixel points in the vector dimension where the digital base map dimension plane matrix is ​​located are selected and arranged to obtain the dimension vectors of windows with different side lengths; wherein, the arrangement order of the dimension vectors of the windows of each side length of each vector dimension is: starting from the edge pixel point in the upper left corner of the window, the data of all edge pixel points of the current vector dimension are arranged in a clockwise order; wherein, the schematic diagram of the dimension vector data arrangement is as follows Figure 2 shown.

[0056] Based on the dimension vectors of windows with different side lengths in each vector dimension, the dimension order offset between each vector dimension is obtained. The obtaining method is:

[0057] For windows with different side lengths, obtain the order of the maximum values ​​in the dimensional vectors of different vector dimensions in the dimensional vectors where they are located as the first maximum order of the dimensional vectors of each vector dimension, and calculate the absolute value of the difference between the first maximum orders of any two different vector dimensions as the dimensional order offset between any two different vector dimensions.

[0058] If the changes in urban geographic space are relatively close in the same space, the calculated data changes will be relatively close, and the calculated urban geographic space dimension order offset value will be relatively small, indicating that the numerical changes in the geographic space information in local areas of the city are relatively similar.

[0059] Furthermore, based on the dimension order offset and the similarity between the dimension vectors, the correlation feature coefficient between each vector dimension and other vector dimensions is calculated, and the acquisition method is:

[0060] For each vector dimension of windows with different side lengths, the similarity between the vector dimension and the dimensional vectors of other vector dimensions is calculated, the product between the dimensional order offset between the vector dimension and the other vector dimensions and the similarity is used as the first product, and the sum of all the first products of the vector dimension is used as the correlation characteristic coefficient of each vector dimension of windows with different side lengths. Among them, this embodiment uses cosine similarity to calculate the similarity between each vector dimension and the dimensional vector of other vector dimensions, and the implementer can select other similarity calculation methods according to actual conditions.

[0061] For the urban information correlation characteristic coefficient of the geographic spatial information under the corresponding vector dimension obtained by summing up multiple different spatial data, if the changes in urban geographic data information under multiple different spaces are relatively close, the calculated values ​​of the urban geographic spatial dimension order offset under different spaces will also be relatively small. At the same time, the similarity between different data vectors is also high. The greater the similarity value between two vectors, the larger the correlation characteristic coefficient calculated under the same vector dimension.

[0062] Furthermore, based on the correlation characteristic coefficients, the city information correlation characteristic coefficients of each vector dimension are obtained, and for each vector dimension, the sum of the correlation characteristic coefficients of all windows in the vector dimension is used as the city information correlation characteristic coefficient of each vector dimension.

[0063] The larger the city information correlation characteristic coefficient is, the higher the correlation between the city geographic spatial data information under the vector dimension and other data information is, that is, the closer the changes of geographic information under spatial attributes in the urban business data warehouse are, the more similar the city business data with similar changes should be stored in an associated manner during the construction of the urban digital base map business data warehouse.

[0064] In the process of building the urban business database, due to the large amount of data information and high data dimension in the urban business database, the data redundancy in the construction of the urban business data warehouse is high and the internal correlation attributes are poor. In the process of searching the urban business data warehouse, the query and retrieval efficiency of related business data is not high.

[0065] Therefore, in the process of constructing the urban business database, it is necessary to further calculate and analyze the urban information correlation characteristic coefficients combining different vector dimension data.

[0066] For each vector dimension in the three-dimensional digital base map matrix, the distance between any two pixel points in the vector dimension is calculated as the first distance. In this embodiment, the Euclidean distance is selected as the metric distance of the first distance. The implementer may use other distances as the metric distance of the first distance.

[0067] Furthermore, for each vector dimension in the three-dimensional digital base map matrix, the product of the first distance between any two pixel points in the vector dimension and the city information association characteristic coefficient of the vector dimension is used as the equivalent distance between any two pixel points.

[0068] Using a clustering algorithm, clustering is performed using the equivalent distance as the metric distance between any two pixel points, and the number of clusters is set to 2 to obtain two clusters. This embodiment uses the k-means clustering algorithm for clustering, and the implementer may select other clustering algorithms according to actual conditions.

[0069] For each cluster, the sum of equivalent clusters between any two pixels in the cluster is calculated as the first equivalent sum, and the set of pixels in the cluster with the smallest first equivalent sum is taken as the urban geographic spatial information data set.

[0070] At this point, the urban geographic spatial information data set of each vector dimension is obtained, and the intersection of the sets of urban geographic spatial information data of all vector dimensions is used as the urban business data set. The flow chart of obtaining the urban business data set is as follows: Figure 3 shown.

[0071] Step S3, completing the construction of the urban spatiotemporal data warehouse based on the urban business data set.

[0072] Taking into account that the city business related data with different vector dimension attributes will also have a corresponding change relationship over time, for the city business data set obtained from the digital base map GIS vector data at each moment, the data in the city business data set is used as the data in the source library, and the ETL tool is used to process the data in the source library, wherein the data processing process includes E aggregation extraction, TC cleaning conversion and L loading, obtaining standard base map data and saving it in the governance library; wherein the ETL tool is a well-known technology and will not be described in detail here; the data in the governance library is processed, and the data that meets the preset standard results requirements is synchronized to the standard library, and other updated and abolished data is saved in the historical library. wherein, when storing the data in the standard library, it is stored in the time sequence of the time when the city business data set is located, and the preset standard results requirements are artificially set and will not be described in detail here.

[0073] At this point, the construction of the urban spatiotemporal data warehouse is completed. The schematic diagram of the construction of the urban spatiotemporal data warehouse is as follows: Figure 4 shown.

[0074] The data correlation of urban geographic spatial information data in the urban spatiotemporal data warehouse is made higher during the data storage process. When querying business data in the urban spatiotemporal data warehouse, the efficiency of business data correlation retrieval in the urban data warehouse is accelerated.

[0075] Based on the same inventive concept as the above method, an embodiment of the present application also provides a business data warehouse construction system for a city digital base map, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the steps of any one of the above-mentioned methods for constructing a business data warehouse for a city digital base map.

[0076] It should be noted that the above sequence of the embodiments of the present application is for description only and does not represent the advantages and disadvantages of the embodiments. The above is a description of a specific embodiment of this specification. In addition, the processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0077] The various embodiments in the present application are described in a progressive manner, and the same or similar parts between the various embodiments can be referenced to each other, and each embodiment focuses on the differences from other embodiments.

[0078] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions, improvements, etc. made within the principles of the present application should be included in the protection scope of the present application.

Claims

1. A method for constructing a business data warehouse of a city digital base map, characterized in that: The method comprises the following steps: Collect various GIS vector data of the city digital base map at each time as each vector dimension; obtain the three-dimensional digital base map matrix of the city digital map at each time; the matrix is ​​composed of two-dimensional geographical location coordinates and each vector dimension at the corresponding coordinate position; Based on the three-dimensional digital base map matrix, dimension vectors of different windows in the digital base map dimension plane matrix of each vector dimension are obtained; based on the difference between the maximum values ​​of the dimension vectors of the same window in the vector dimension, the dimension sequence offset between any two different vector dimensions of the same window is obtained; Based on the dimension order offset and the similarity between the dimension vectors, the correlation feature coefficients between each vector dimension and all other vector dimensions of the same window are obtained; Based on the correlation characteristic coefficient, obtain the city information correlation characteristic coefficient of each vector dimension; based on the city information correlation characteristic coefficient, obtain the city business data set of each vector dimension; Build an urban spatiotemporal data warehouse based on urban business data sets.

2. The method for constructing a business data warehouse of a city digital base map according to claim 1, characterized in that: The GIS vector data includes: terrain height, building density, traffic volume, population density, number of shopping malls and number of schools.

3. The method for constructing a business data warehouse of a city digital base map according to claim 1, characterized in that: The digital base map dimension plane matrix includes: The two-dimensional matrix under each vector dimension in the three-dimensional digital base map matrix serves as the digital base map dimension plane matrix of each vector dimension.

4. The method for constructing a business data warehouse of a city digital base map according to claim 1, characterized in that: The method for obtaining the dimension vector is: For the digital base map dimension plane matrix of each vector dimension in the three-dimensional digital base map matrix, a window with different preset side lengths is constructed with the central pixel point of the digital base map dimension plane matrix as the center; For windows with different preset side lengths, the data of the window edge pixels in the digital base map dimension plane matrix are selected to construct the dimension vectors of the corresponding vector dimensions in windows with different preset side lengths.

5. The method for constructing a business data warehouse of a city digital base map according to claim 4, characterized in that: The method for obtaining the dimension sequence offset is: For windows with the same preset side length, obtain the order of the maximum value in the dimensional vector of each vector dimension as the first maximum order of the dimensional vector of each vector dimension, and calculate the absolute value of the difference between the first maximum orders of any two different vector dimensions as the dimensional order offset between any two different vector dimensions.

6. The method for constructing a business data warehouse of a city digital base map according to claim 4, characterized in that: The method for obtaining the correlation characteristic coefficient is: In any window with the same preset side length, for any vector dimension, calculate the similarity between the dimensional vectors of any vector dimension and other vector dimensions, take the product of the dimensional sequence offset between any vector dimension and other vector dimensions and the similarity as the first product, and take the sum of all the first products of any vector dimension as the associated characteristic coefficient of any vector dimension in the same window.

7. The method for constructing a business data warehouse of a city digital base map according to claim 4, characterized in that: The method for obtaining the city information association characteristic coefficient is: For each vector dimension, the sum of the correlation characteristic coefficients of all windows in the vector dimension is used as the city information correlation characteristic coefficient of each vector dimension.

8. The method for constructing a business data warehouse of a city digital base map according to claim 1, characterized in that: The method for obtaining the city business data set is: For each vector dimension in the three-dimensional digital base map matrix, the distance between any two pixel points in the vector dimension is calculated as the first distance; The product of the first distance between any two pixel points in the vector dimension and the city information association characteristic coefficient in the vector dimension is taken as the equivalent distance between any two pixel points; Using a clustering algorithm, clustering is performed by taking the equivalent distance as the metric distance between any two pixel points to obtain a preset number of clusters; For each cluster, the sum of equivalent clusters between any two pixels in the cluster is calculated as the first equivalent sum, and the set of pixels in the cluster with the smallest first equivalent sum is taken as the urban geographic spatial information data set.

9. The method for constructing a business data warehouse of a city digital base map according to claim 1, characterized in that: The construction of the urban spatiotemporal data warehouse according to the urban business data set includes: For the urban business data set obtained from the digital base map GIS vector data at each moment, the data in the urban business data set is used as the data in the source library, and the ETL tool is used to process the data in the source library to obtain standard base map data and save it in the governance library; The data in the governance library is processed, and the data that meets the preset standard results requirements are synchronized to the standard library in the chronological order of the time when the urban business data set is located. Other updated and invalidated data are saved in the historical library to complete the construction of the urban spatiotemporal data warehouse.

10. A business data warehouse construction system for a city digital base map, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the computer program, the steps of the method for constructing a business data warehouse for a city digital base map as described in any one of claims 1 to 9 are implemented.